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• VCMMG368

  Use the unit circle to define trigonometric functions as functions of a real variable, and graph them with and without the use of digital technologies

  Elaborations

  • establishing the symmetrical properties of trigonometric functions
  • investigating angles of any magnitude
  • understanding that trigonometric functions are periodic and that this can be used to describe motion
  • identifying points on the unit circle via arc lengths in radians, which correspond to specified values of the circular functions sine, cosine and tangent

  VCMMG368 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• VCMNA364

  Solve simultaneous equations using systematic guess-check-and-refine with digital technology

  Elaborations

  • using graphs to determine a convergent set of intervals which contain a point of intersection of the graphs of two functions
  • using cobweb diagram to solve simultaneous equations numerically

  VCMNA364 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VCMSP373

  Use digital technology to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation, make predictions based on this straight line and discuss limitations

  Elaborations

  • investigating different techniques for finding a ‘line of best fit’
  • using a fitted line to data to make predictions between and beyond existing data value sand discuss limitations of these predictions

  VCMSP373 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• VC2M10AA08

  use function notation to describe the relationship between dependent and independent variables in modelling contexts

  Elaborations

  • identifying independent and dependent variables in modelling contexts and representing the relation between them using tables, graphs and rules
  • using technology to draw graphs of functions defined using function notation with consideration of domain and range

  VC2M10AA08 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMNA363

  Use function notation to describe the relationship between dependent and independent variables in modelling contexts

  Elaborations

  • identify independent and dependent variables in modelling contexts and represent the relation between them using tables, graphs and rules
  • using technology to draw graphs of functions defined using function notation with consideration of domain and range

  VCMNA363 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VC2M10AST02

  identify measures of spread, and understand their interpretation and usefulness with respect to different data distributions

  Elaborations

  • comparing the use of quantiles, percentiles, and cumulative frequency to analyse the distribution of data
  • comparing measures of spread for different data distributions, such as mean or median absolute deviations with standard deviations, and exploring the effect of outliers

  VC2M10AST02 | Mathematics | Mathematics Version 2.0 | Level 10A | Statistics

• VC2M10ASP06

  design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions 

  Elaborations

  • designing and making scale models of three-dimensional objects using digital tools; for example, making components of a puzzle using a three-dimensional printer, and planning and designing the puzzle using principles of tessellations
  • applying a computational thinking approach to solving problems involving networks, for example, connectedness, coverage and weighted measures, such as taking different routes and choosing the most efficient route to take when travelling by car using virtual map software 
  • defining and decomposing spatial problems, creating and applying algorithms to generate solutions, and evaluating and communicating solutions in terms of the problem; for example, designing a floor plan for a department store that limits congestion at key areas such as check-outs, changing rooms and near popular sale items
  • designing, creating and testing algorithms using pseudocode or flow charts for producing self-similar patterns; and validating algorithms using a range of test cases to compare their output
  • exploring geospatial technologies used by Aboriginal and/or Torres Strait Islander communities, to consider spatial problems including position and transformation

  VC2M10ASP06 | Mathematics | Mathematics Version 2.0 | Level 10A | Space

• VC2M10AA06

  apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

  Elaborations

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors

  VC2M10AA06 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMNA361

  Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

  Elaborations

  • investigating the features of graphs of polynomials including axes intercepts and the effect of repeated factors

  VCMNA361 | Mathematics | Level 10A | Number and Algebra | Linear and non-linear relationships

• VC2M10AA02

  devise and use algorithms and simulations to solve mathematical problems

  Elaborations

  • applying a systematic guess-check-and-refine algorithm to identify an approximate value for the root of an equation in an interval
  • developing simulations for counterintuitive problems in probability such as the Monty Hall problem or derangements

  VC2M10AA02 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMNA358

  Devise and use algorithms and simulations to solve mathematical problems

  Elaborations

  • applying a systematic guess-check-and-refine algorithm to identify an approximate value for the root of an equation in an interval
  • developing simulations for counter-intuitive problems in probability such as the Monty Hall problem or derangements

  VCMNA358 | Mathematics | Level 10A | Number and Algebra | Patterns and algebra

• VC2M10AM01

  solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids

  Elaborations

  • using formulas to solve problems
  • using authentic situations to apply knowledge and understanding of surface area and volume

  VC2M10AM01 | Mathematics | Mathematics Version 2.0 | Level 10A | Measurement

• VCMMG365

  Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids

  Elaborations

  • using formulas to solve problems
  • using authentic situations to apply knowledge and understanding of surface area and volume

  VCMMG365 | Mathematics | Level 10A | Measurement and Geometry | Using units of measurement

• VC2M10AN01

  define rational and irrational numbers and perform operations with surds and fractional indices

  Elaborations

  • understanding that the real number system includes irrational numbers
  • extending the exponent laws to rational number indices
  • performing the 4 operations with surds

  VC2M10AN01 | Mathematics | Mathematics Version 2.0 | Level 10A | Number

• VCMNA355

  Define rational and irrational numbers and perform operations with surds and fractional indices

  Elaborations

  • understanding that the real number system includes irrational numbers
  • extending the index laws to rational number indices
  • performing the four operations with surds

  VCMNA355 | Mathematics | Level 10A | Number and Algebra | Real numbers

• VC2M10AP01

  explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities

  Elaborations

  • applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
  • understanding that a set with n elements has 2ⁿ different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table; for example, the set {a, b, c} has 2³ = 8 subsets which are { ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
  • using the definition of n! to represent and calculate in contexts that involve choices from a set; for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement?
  • performing calculations on numbers expressed in factorial form, such as n!r! to evaluate the number of possible arrangements of n objects in a row, r of which are identical; for example, 5 objects, 3 of which are identical, can be arranged in a row in
    5!3!=5×4×3×2×13×2×1= 20 different ways

  VC2M10AP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability